Model-updating for self-adjoint quadratic eigenvalue problems

This paper concerns quadratic matrix functions of the form L(λ)=Mλ2+Dλ+K where M,D,K are Hermitian n×n matrices with M>0. It is shown how new systems of the same type can be generated with some eigenvalues and/or eigenvectors updated and this is accomplished without “spill-over” (i.e. other spectral data remain undisturbed). Furthermore, symmetry is preserved. The methods also apply for Hermitian matrix polynomials of higher degree.